The first integral term gives the scattered field due to one interaction within the heterogeneity, the second to two interactions within the heterogeneity, etc. The scattered field is now expressed in terms of the background field only. Eventually, all multiple-scattering orders can be incorporated into a transition operator \({\bf T}\) , hereafter called T-operator\({\bf T}\)  is called here the T-operator to avoid the confusion with the T-matrix, which, in the numerical method of the same name [1]}, is generally defined in a basis of vector spherical wave functions., such that
\({\bf E}_\text{s}({\bf r}) = \int {\bf G}_\text{b}({\bf r},{\bf r}^{\prime }) {\bf T}({\bf r}^{\prime },{\bf r}^{\prime \prime }) {\bf E}_\text{b}({\bf r}^{\prime \prime }) d{\bf r}^{\prime } d{\bf r}^{\prime \prime }. \) 
